The heterogeneity of tumor cell populations is instrumental in treatment failure an the inability to develop curative protocols. The emergence of drug resistant cells, their overgrowth, and their possible resensitization are major contributors to the extent and impact of this heterogeneity. Recent technical advances have already produced extraordinary new data for one particular mode of resistance: that due to increased dihydrofolate reductase (DHFR) content obtained during the selection pressure of methotrexate treatment. The availability of fluorescent enxyme binding techniques and high speed flow systems permit the classification and selection of individual cells by DHFR content, and new insights have already been gained into the direct gene control of DHFR synthesis. The amplified genes have been shown to be contained in double minute "chromosomes" and the homogeneous staining region of chromosomesin resistant cells. These new findings, and other, suggest that forthis system it is now possible to model and quantify the emergence and reversion of elevated reductase resistance in populations of cancer cells. The intent of our grant is to use mathematical models to investigate the plausibility of candidate mechanisms of gene amplification and the role of reductase-related growth in the propagation of resistance including the effects of the presence of drug. Mechanisms responsible for both double minutes and homogeneous staining regions will be modeled and evaluated against double minute and dihydrogolate reductase requency distributions. These models supported by collaborative measurements obtained by Dr. R. Schimke and Dr. Brown at Stanford, Dr. P. Barker at Yale, nd Dr. R. Kaufman at M.I.T. will describe in a realistic way the growth and enzyme dynamics of a heterogeneous population of target cells undergoing long-term drug treatment. Preliminary studies have already led to estimates of double minute production and loss rates in human carcinoma cells.